Sitting in a shack that totters on stilts in a slum overlooking Bogotá, Colombia's capital city, Gloria Torres gasps as she looks at the creased and faded photograph of her son. He is smiling slightly, dressed in his best, thumbs in pockets, his dark eyes soft.

Torres holds it to her chest, crumples, seems to shrink by half in less than a second, then remembers she has guests. She composes herself, and lays the photo carefully back in a shoebox and strokes the face, brushes down her apron and pulls her youngest daughter closer. In a gentle, determined voice, she begins to tell her family's story.

Torres will remember 7 June 2007 for the rest of her life. She can even pinpoint the hour she knew that her son, 17-year-old Aurelio, was dead.

"It was 3am. I felt something, like he'd come home, come to my bedside. I awoke and spoke to him, but he wasn't there. Then a feeling, a pain came over me, which to this day I still can't shake off."

In Colombia, torn apart by decades of civil war, premonitions of deaths foretold are often heeded.

"Later, I found out that at that very moment the army were assassinating him," she says.

Colombia's conflict is a three-way standoff between the leftist Farc (the Revolutionary Armed Forces of Colombia) guerrillas, the government, which is represented by the military, and paramilitary groups founded by wealthy Colombian landowners. And swept up in this conflict in the most brutal manner are ordinary families.

The Farc was formed in the 1960s by peasants after government soldiers attacked rural communist enclaves, and today numbers about 10,000 men, women and children. They face down the Colombian military, funded by the US under its Plan Colombia, an anti-drugs and counter-insurgency initiative introduced by the Clinton administration.

In the 80s, as the Farc gained territory, wealthy Colombian land-owners formed paramilitary groups (United Self-Defence Forces of Colombia, or AUC) to defend their property. But the brutal, pro-government groups of the AUC were little more than death squads, often carrying out the government's dirty work.

In this crossfire are the campesinos, the rural poor. Unluckily for Torres, the soldiers wanted a combat kill to please commanders. They are rewarded with cash or holidays for killing guerillas but, essentially, any corpse will do in this dirty war. They had intended to bury Aurelio as a "no name" (NN), an unknown guerrilla combatant, but a friend of the boy identified his body at the graveyard.

"There are so many mothers here in the same situation, who have lost their sons as NNs," says Torres.

She says an ex-paramilitary commander admitted that his men killed many boys like her son, and presented them to the army. They charged 4m pesos [£1,350].

"That's what my son was worth – 4m pesos," says Torres.

She shoos her daughter out of the room. "Sometimes, when I'm out walking here, I think I see him. I always think I'll see him, every day. Then I have to remember again that he is dead," she says.

Although most of these killings remain largely unreported around the world, one particularly brutal event in another part of the country sparked a macabre international cause celebre. In October 2008, 11 young men were enticed away from their homes in Soacha, a poor suburb of Bogotá, and offered work. A few weeks later, they were found in a grave in Ocaña, near the border of Venezuela, dressed in Farc uniforms and presented as dead guerrillas.

The Soacha killings prompted Philip Alston, the United Nations special rapporteur on extrajudicial executions, to say: "… while the Soacha killings were undeniably blatant and obscene … they are but the tip of the iceberg." The practice, he said, was "carried out in a more or less systematic fashion by significant elements within the military."

The mothers of the dead men, Los Madres de Soacha (The Mothers of Soacha), as they are known, have been campaigning for justice ever since and are still receiving death threats. Nevertheless, one of the women, María Ubilerma Sanabria, recently called for every mother in Colombia who has suffered as they have to stand up and report their loss without fear: "We are women, poor and fighting against the government, which refuses to recognise its responsibility, but we will not surrender."

Los Madres de Soacha may be a particularly stark example of Colombia's bitter internal strife, but this is a family tragedy that knows no boundaries and touches the old and young alike.

Claudia Ortega is still fighting for justice for her mother, Maria, who was shot at her home in Vista Hermosa, in the Meta province, a hotspot for attacks. The army surrounded her mother's home on 4 June 2007. That day, a group of guerrillas were seen crossing the patio of her home, and the army, using heavy artillery from the ground and helicopters, destroyed the house. A bullet blasted through her mother's neck, according to medical records.

When Claudia searched her mother's home, she found a trail of blood from the first floor down to the ground floor. Her mother's body was not there, but had been taken away and buried. The army had claimed she was a guerrilla, and buried her in a graveyard in La Macarena, a few hours' drive away.

"My mother had nothing to do with the guerrillas. They said she gave medical support to them, but she was a farmer. She didn't even know how to give an injection," says Ortega.

Claudia's husband, Elias, says the army has no respect for civilians in areas where guerrillas operate, accusing them of collaboration. "They don't care about us as people. They just want to say, 'We killed 20, 30 guerrillas', and get the promotions. If what they say was true, there'd be no guerrillas left and the war would be over."

That same day, the army claimed to have killed 12 guerrillas, including a cousin of Elias. "Only four of those men were guerrillas. The rest were local boys who were cleaning the channels by the side of the road. But by the time the families got to the graveyard, they were already buried," he says.

Getting their story heard is the hardest part, says Elias: "The government say human rights lawyers pay us to say this, that we are liars, that we collaborate. But they are the liars. We respect the state, but we reject their criminal actions. I swear to you that this is true."

It is a fact that soldiers of the Colombian army killed Aurelio Torres and Maria Ortega and that they were not guerrillas. In Torres's case, the army have admitted that much, though no one has been punished for the crime. The question to which there is no humane answer is why. An answer does exist, but is so shocking as to seem fictional: thanks to a government decree, Colombian soldiers received bonuses, holidays and promotions linked to the number of guerrillas they killed.

Up to 3,000 Colombian civilians have been killed by government forces and paramilitaries in a phenomenon known as "false positives", where innocent people are extrajudicially executed and presented as guerrillas to army chiefs who reward results, no matter how they are achieved.

Sometimes the army present the dead with a weapon or a grenade, and often, after killing them, their assassins dress them in Farc uniforms. The soldiers and their hitmen can be cavalier – presenting the bullet-riddled corpses in unused boots too big for their feet, their fatigues fresh and unmarked.

The impact of the civil war on the lives of ordinary Colombian families is well-documented by Amnesty International and other organisations. Marcelo Pollack, of Amnesty, says the need for results in the war has "created the environment in which many soldiers felt they had a green light to execute civilians with impunity". This, he says, means Colombian civilians have been constantly subject to human-rights violations.

"What has marked the Colombian armed conflict over the past 45 years has been the complete failure of all the parties to the conflict, whether they be army soldiers, the guerrilla or paramilitary groups, to respect the right of civilians not to be dragged into the hostilities," says Pollack.

According to John Lindsay-Poland, of the Fellowship of Reconciliation, a faith-based NGO that campaigns on human-rights issues in Latin America, "The Colombian state has long framed its war against guerrillas as a war against narcoterrorism. The war on drugs is combined with Colombia's long-running dirty war on people," he says. "The same army units that are fighting guerrillas involved in the drugs trade also have killed many civilians.

"The shocking thing about the false positives was it took it to a new level," he adds. "It wasn't just targeting social leaders or activists, it was people who might be easily forgotten. The military thought if we pick up someone – someone who wouldn't be missed, or people whose families have no political or economic sway – we add to the bodycount. It grows out of the social inequalities in the country that are so deep. Some people can just be forgotten."

He could be talking about the grandfather of 26-year-old Sol Milena Cordoba, a poor, uneducated woman from San José del Guaviare. Cordoba is eight months pregnant, and one of a number of people who have travelled to a safe house in La Macarena to tell me their stories. It is swelteringly hot and there are soldiers on every corner, M16s primed, faces blank, but still people risk coming to speak of their shattered families.

Cordoba's grandfather was shot on 17 April 2008 by soldiers of the national army's 7th Mobile division. "My grandfather left the house that day with my eldest son, as he lived with them. He didn't know there were soldiers along the way. They shot him in front of my son. They covered the child with dust and blood. He says he screamed and cried for his grandfather, that he couldn't stop screaming. He thought they'd shoot him, too.

"They killed my grandfather just because they felt like it. They shot him from seven metres away. He was wearing normal clothes, not a guerrilla uniform. After they shot him, they stripped him and buried his clothes in the road.

"Later, friends brought my son to me. That night, he cried until he went to sleep and cried as soon as he woke up, shouting for his grandfather. He always cries whenever we speak about it. He tells stories about him and cries. My grandmother died six months later."

In La Macarena, the pain of losing a family member in these circumstances is, unimaginably, sharpened. On a field next to the packed red earth of the military airport's runway, there is a huge, unregulated grave site adjoining the municipal cemetery. In this field, hundreds of people have been buried in individual, unmarked graves, killed by the army, claimed as combat kills. But civilians for hundreds of miles around say their innocent family members lie beneath the scrub.

These families cannot even claim their loved ones' remains or seek justice, as the army's practice of burying the dead as anonymous guerrillas means there is no identified corpse. They have simply disappeared. All the legal and medical mechanisms to exhume and investigate exist, but the political will to do so is lacking. Instead, campaigners, journalists and victims connected to the cases are acused by the government of collaboration with guerrilla groups.

In Argentina in the 80s, Morris Tidball-Binz of the International Committee of the Red Cross, was the first forensic scientist to bring that area of expertise to the world's killing fields. A group of grandmothers were demanding an investigation into the disappearance of thousands of their family members wiped out in military purges, and sought the help of forensic scientists, who set up the Argentine Forensic Anthropology Team (EAAF). He says Colombia is not doing enough in respect of La Macarena graveyard, and that without due process, families "endure a limbo of uncertainty".

"A lot has been done in Colombia, [that] has to be acknowledged, but more remains to be done, and urgently," he says.

Luis Fondebrider, the current head of the EAAF, says identifying the dead gives relatives peace and emotional respite.

"The process of exhuming and identifying the remains of disappeared people has made it possible for people, after years of uncertainty, to know what happened to their loved ones. They can give them a dignified burial, they can have a place in the cemetery where they can visit, and in some way, it gives people who were stripped of their rights their name back. It's like they enter society once more," he says.

As the day in La Macarena draws to a close, there is one last person for me to meet, one final story to hear.

Vladimir Rubiano, a farmer in La Macarena, has the face of a prize-fighter and the manners of an aristocrat. After waiting six hours to talk to me, he waves away apologies with massive hands and a broad grin.

His meticulous account of the death of his nephew, shot by the army on 14 March 2009, takes an hour. The child was carrying a small hunting rifle, common in the rural areas, but twitchy state troops shot him dead. As the testimony draws to an end, I ask Rubiano what the future might hold for his son, a four-year-old sitting calmly on his knee, listening. What dreams does he have for him?

"Oh, he's not my son. The guerrilla killed his father. I raise him now," he says. "We're caught here, stuck in the middle of this war," he says. "Attacked by all sides. We just want peace."